Optimal control of vibrational transitions of HCl

Control of fundamental and overtone transitions of a vibration are studied for the diatomic molecule, HCl. Specifically, the results of the effect of variation of the penalty factor on the physical attributes of the system (i.e., probabilities) and pulse (i.e., amplitudes) considering three different pulse durations for each value of the penalty factor are shown and discussed. We have employed the optimal control theory to obtain infrared pulses for selective vibrational transitions. The optimization of initial guess field with Gaussian envelope, phrased as maximization of cost functional, is done using the conjugate gradient method. The interaction of the field with the molecule is treated within the semiclassical dipole approximation. The potential and the dipole moment functions used in the calculations of control dynamics are obtained from high level ab-initio calculations.     

Two-soliton and three-soliton interactions of electron acoustic waves in quantum plasma

The overtaking collision between electron acoustic multisolitons in an unmagnetized quantum plasma consisting of ions, and both hot and cold electrons has been investigated. The Hirota bilinear method is employed to study phase shifts and trajectories during the overtaking collision of multisolitons. It is observed that phase shifts are significantly affected by the quantum parameter H. The phase shifts are proportional to B^1/3 (dispersion coefficient) and are functions of their respective amplitudes. It is also seen that the soliton structure occurs only if H < 2.     

A class of degenerate stochastic differential equations with non-Lipschitz coefficients

We obtain sufficient condition for SDEs to evolve in the positive orthant. We use arguments based on comparison theorems for SDEs to achieve this. As an application we prove the existence of a unique strong solution for a class of multidimensional degenerate SDEs with non-Lipschitz diffusion coefficients.     

Bianchi type-V string cosmological models in general relativity

Bianchi type-V string cosmological models in general relativity are investigated. To get the exact solution of Einstein’s field equations, we have taken some scale transformations used by Camci et al [Astrophys. Space Sci. 275, 391 (2001)]. It is shown that Einstein’s field equations are solvable for any arbitrary cosmic scale function. Solutions for particular forms of cosmic scale functions are also obtained. Some physical and geometrical aspects of the models are discussed.     

On the elliptic flow for nearly symmetric collisions and nuclear equation of state

We present the results of elliptic flow for the collision of nearly symmetric nuclei (₁₀Ne²⁰+ ₁₃Al²⁷_{10}{\rm Ne}^{20}+\,_{13}{\rm Al}^{27}, ₁₈Ar⁴⁰+ ₂₁Sc⁴⁵_{18}{\rm Ar}^{40}+\,_{21}{\rm Sc}^{45}, ₃₀Zn⁶⁴+ ₂₈Ni⁵⁸_{30}{\rm Zn}^{64}+\,_{28}{\rm Ni}^{58}, ₃₆Kr⁸⁶+ ₄₁Nb⁹³_{36}{\rm Kr}^{86}+\,_{41}{\rm Nb}^{93}) using the quantum molecular dynamics (QMD) model. General features of elliptic flow are investigated with the help of theoretical simulations. The simulations are performed at beam energies between 45 and 105 MeV /nucleon. A significant change can be seen from in-plane to out-of-plane elliptic flow of different fragments with incident energy. A comparison with experimental data is also made. Further, we show that elliptic flow for different fragments follows power-law dependence as given by the function C(A_tot)^tC{(A_{\rm tot})^\tau}.     

Long term performance evaluation of the TACTIC imaging telescope using ∼400 h Crab Nebula observation during 2003–2010

The TeV atmospheric Cherenkov telescope with imaging camera (TACTIC) γ-ray telescope has been in operation at Mt. Abu, India since 2001 to study TeV γ-ray emission from celestial sources. During the last 10 years, apart from consistently detecting a steady signal from the Crab Nebula above ～1.2 TeV energy, at a sensitivity level of ～5.0 σ in ～25 h, the telescope has also detected flaring activity from Mrk 421 and Mrk 501 on several occasions. Although we used Crab Nebula data partially, in some of the reported results, primarily for testing the validity of the full data analysis chain, the main aim of this work is to study the long term performance of the TACTIC telescope by using consolidated data collected between 2003 and 2010. The total on-source data, comprising ～402 h, yields an excess of ～(3742±192) γ-ray events with a statistical significance of ～19.9 σ. The off-source data, comprising ～107 h of observation, is found to be consistent with a no-emission hypothesis, as expected. The resulting γ-ray rate for the on-source data is determined to be ～(9.31±0.48) h ^?1. A power law fit (dΦ/dE=f ₀ E ^?Γ ) with f ₀ ～ (2.66±0.29) × 10^?11 cm^?2 s^?1 TeV^?1 and Γ ～ 2.56±0.10 is found to provide reasonable fit to the inferred differential spectrum within statistical uncertainties. The spectrum matches reasonably well with that obtained by other groups. A brief summary of the improvements in the various subsystems of the telescope carried out recently, which has resulted in a substantial improvement in its detection sensitivity (viz., ～5 σ in an observation period of ～13 h as compared to ～25 h earlier) are also presented in this paper. Encouraged by the detection of strong γ-ray signals from Mrk 501 and Mrk 421 on several occasions, there is considerable scope for the TACTIC telescope to monitor similar TeV γ-ray emission activity from other active galactic nuclei on a long-term basis.     

Subwavelength propagation and localization of light using surface plasmons: A brief perspective

Surface plasmons at the metal–dielectric interface have emerged as an important candidate to propagate and localize light at subwavelength scales. By tailoring the geometry and arrangement of metallic nanoarchitectures, propagating and localized surface plasmons can be obtained. In this brief perspective, we discuss: (1) how surface plasmon polaritons (SPPs) and localized surface plasmons (LSPs) can be optically excited in metallic nanoarchitectures by employing a variety of optical microscopy methods; (2) how SPPs and LSPs in plasmonic nanowires can be utilized for subwavelength polarization optics and single-molecule surface-enhanced Raman scattering (SERS) on a photonic chip; and (3) how individual plasmonic nanowire can be optically manipulated using optical trapping methods.     

The cohomology of orbit spaces of certain free circle group actions

Suppose that \(G =\mathbb{S}^1\) acts freely on a finitistic space X whose (mod p) cohomology ring is isomorphic to that of a lens space \(L^{2m-1}(p;q_1,\ldots,q_m)\) or \(\mathbb{S}^1\times \mathbb{C}P^{m-1}\). The mod p index of the action is defined to be the largest integer n such that α ⁿ ?≠?0, where \(\alpha \,\epsilon\, H^2(X/G;\mathbb{Z}_p)\) is the nonzero characteristic class of the \(\mathbb{S}^1\)-bundle \(\mathbb{S}^1\hookrightarrow X\rightarrow X/G\). We show that the mod p index of a free action of G on \(\mathbb{S}^1\times \mathbb{C}P^{m-1}\) is p???1, when it is defined. Using this, we obtain a Borsuk–Ulam type theorem for a free G-action on \(\mathbb{S}^1\times \mathbb{C}P^{m-1}\). It is note worthy that the mod p index for free G-actions on the cohomology lens space is not defined.     

An <Emphasis Type="BoldItalic">n</Emphasis>-dimensional pseudo-differential operator involving the Hankel transformation

An n-dimensional pseudo-differential operator (p.d.o.) involving the n-dimensional Hankel transformation is defined. The symbol class H ^m is introduced. It is shown that p.d.o.’s associated with symbols belonging to this class are continuous linear mappings of the n-dimensional Zemanian space H_m(Iⁿ)H_\mu(I^n) into itself. An integral representation for the p.d.o. is obtained. Using the Hankel convolution, it is shown that the p.d.o. satisfies a certain L ¹-norm inequality.     

Complex dynamical invariants for two-dimensional complex potentials

Complex dynamical invariants are searched out for two-dimensional complex potentials using rationalization method within the framework of an extended complex phase space characterized by x?=?x ₁?+?i p ₃,?y?=?x ₂?+?i p ₄, ?p _x ?=?p ₁?+?i x ₃, ?p _y ?=?p ₂?+?i x ₄. It is found that the cubic oscillator and shifted harmonic oscillator admit quadratic complex invariants. The obtained invariants may be useful for studying non-Hermitian Hamiltonian systems.